Using second-order approximation to incorporate GCM uncertainty in climate change impact assessments

This study presents a method to incorporate uncertainty of climate variables in climate change impact assessments, where the uncertainty being considered refers to the divergence of general circulation model (GCM) projections. The framework assesses how much bias occurs when the uncertainties of climate variables are ignored. The proposed method is based on the second-order expansion of Taylor series, called second-order approximation (SOA). SOA addresses the bias which occurs by assuming the expected value of a function is equal to the function of the expected value of the predictors. This assumption is not valid for nonlinear systems, such as in the case of the relationship of climate variables to streamflow. To investigate the value of SOA in the climate change context, statistical downscaling models for monthly streamflow were set up for six hydrologic reference stations in Australia which cover contrasting hydro-climate regions. It is shown that in all locations SOA makes the largest difference for low flows and changes the overall mean flow by 1–3%. Another advantage of the SOA approach is that the individual contribution of each climate variable to the total difference can be estimated. It is found that geopotential height and specific humidity cause more bias than wind speeds in the downscaling models considered here.